Using three values of the differential exponent, namely 2.65, 2.70 and 2.75, of the primary cosmic-ray nucleon spectrum, the scaling model of high-energy N-N collisions parametrised from the recent ISR data and a realistic model for the propagation of cosmic rays through the atmosphere, the sea-level vertical muon spectra in the energy range 0.5-103 GeV have been derived. By comparing the results with the recent muon data of Allkofer et al. (1971) it can be concluded that the primary cosmic-ray nucleon spectrum may be represented by a single exponent over the whole energy range 5-104 GeV, and is given by the relation D(EN)dEN=2.48E N-2.70dEN. This conclusion is not in agreement with the results of some recent similar calculations.

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University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Primary cosmic-ray nucleon spectrum from the sea-level muon spectrum using the scaling model

Journal of Physics G: Nuclear Physics

The energy distributions of primary cosmic-ray nucleons responsible for muons detected at sea level and underground have been calculated using a phenomenological model. The Feynman scaling hypothesis of nucleon-nucleon interactions has been employed using cross sections determined from high-energy scattering experiments.

Energy distribution of parent nucleons for muons observed at sea level and underground

In view of a number of contrasting results from calculations of the charge ratio of vertical cosmic-ray muons at sea level, a precise calculation has been carried out over the muon energy range 1-104 GeV using a realistic phenomenological model. It involves the energy spectrum and mass composition of primary cosmic rays, a scaling model basically fitted to ISR p-p inclusive data and applied to primary air-nucleus collisions with some special attention, and a model for the cosmic-ray cascade through the atmosphere. The calculated muon charge ratio and its variation with energy can be made to agree with worldwide measurements by adjusting realistically the n/p ratio in the primary flux with spectral exponent gamma =2.7 and the probability of nucleon charge retention in N-N collisions, and also invoking a 25% charge exchange probability in p-n collisions inside the nucleus. A critical analysis of the results of calculations by different authors with reference to this procedure has been made and the reasons for apparently discordant conclusions are indicated.

Interpretation of the charge ratio of vertical cosmic-ray muons at sea level

An important numerical consequence of a recent calculation of the correlation between the energy spectra of primary cosmic-ray nucleons and sea-level muons using the scaling model is reported. The consequence interrelates between the energies of the two cosmic-ray species and may be stated specifically as Emedian=6.9(Emu+2) in contrast to the customary relation Emedian=10Emu, where E median is the median energy of primary nucleons responsible for sea-level muons of specific energy Emu.

The intercalation between the primary cosmic-ray nucleon and sea-level muon energies using the scaling model

The integral energy spectrum of all primary cosmic-ray particles in the energy range 50-106 GeV presented by Grigorov et al. (1970, 1971) in a series of proton satellite experiments has been used to derive the differential energy spectrum of primary cosmic-ray nucleons with the help of the recent knowledge of the mass composition of primary cosmic rays. It is found to be represented by the form D(EN)=2.06EN -2.70cm-2 sr-1 s-1 GeV-1 over the nucleon energy range 50-104 GeV. This form D(E N)=2.54 EN-2.60, suggested by Hoock and Turver (1974) from the experimental results of Grigorov et al. and used extensively by Bhattacharyya and his collaborators (1977) to derive the secondary cosmic-ray spectra, is not justified.

Journal	Journal of Physics G: Nuclear Physics
Publisher	-
ISSN	0305-4616